Finite Group Databasebeta

C4×#15689383 #26223137

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#15689383

Splittings

FittingC2×C4×SD16×C47 ⋊ C2
SylowC47 ⋊ C4×#471

Subgroups

subgroupG/H
centerC2×C4#13093995
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×SD16×C47C2
socleC22×C47C2×#121
prime radicalC2×#13094050C22
cosocleC22×C4×C47C24
hypercenterC2×C4×SD16D47
hypocenterC47C4×#471
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

914 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 176427);